I believe in the Bahá'í Faith primarily because of the history. Just as Christ, Mohammad, Moses, Abraham, The Buddha, etc., actually lived on this earth and taught of divinity, so too did Bahá'u'lláh and the Báb were founders of our Faith.
Bahá'u'lláh teaches that all these religions come from God, that they are all true. Yet, differences have arisen because religions have always attempted to meet the needs of the people at the time. What was necessary in 1 BC was different from the needs of 600 CE and 600 BC (for example). There's that, and all the ways that people have mutilated religion and its purpose to serve their own interest. These two reasons are primarily why many religions appear different. In reality, they are one in the same.
Okay, so why do I believe Bahá'u'lláh and the Báb were prophets? There are a few reasons.
For one, reading the their writings illuminates subjects for me in a deep way. For example: the nature of life after death, the soul, the nature of God, the Prophets, prophecy, etc.
Second, the character of Bahá'u'lláh and the Báb, and their followers, as recorded by history. Bahá'u'lláh, for example, was born into a wealthy family in a prominent position in Persia when the government was extremely corrupt (perhaps even moreso than today). Yet, he gave up these worldly things to protect the oppressed and give to the poor. He followed the teachings of the Báb (Who we also consider a Prophet, and foretold the coming of Bahá'u'lláh), and was imprisoned for being a loyal follower. He went on to live most of His life in exile and a prisoner -- yet all this did not deter Him from spreading a message from God, calling for the unity of all mankind, and revealing countless tablets. When one considers the history, we see that at all times the government of Persia, that of modern-day Iraq and of Constantinople tried to silence Him, but yet despite this He still created a world-wide religion.
Lastly, there's a more personal component to belief, which I suspect most religious people share in some way. It's a spark of faith that can only be experienced, not described. I think it's latent in all of us as we all have a spiritual existence in addition to the mortal one we perceive. I don't try to use this to justify my faith to anyone. I think, for many, this comes from prayer and experiences in life.
My parents were Bahá'ís too, but they didn't really raise me to be one. Sure, they took me to Bahá'í classes on a few occasions, but not many. Really it became part of my identity when I was in college.